In ref. [1]}, we proposed a gauged \(U(1)_{\mu - \tau }\)  model in which interactions among \(Z^{\prime }\)  and quarks are radiatively generated via one-loop diagram with
vector-like quarks(\(Q^{\prime }\) ) and scalar dark matter(DM) candidate propagating inside loop See also refs. [2]}, [3]}, [4]}, [5]} for similar mechanism and analysis.
Also scenarios in which vector-like fermions are mixed with the SM fermions are also found e.g. in refs. [6]}, [7]}..
In this work, we focused on a loop diagram associated with
\(Z^{\prime }Q^{\prime }\bar{Q}^{\prime }\)  interaction.
But there are contributions associated with \(Z Q^{\prime } \bar{Q}^{\prime }\)  and photon\(-Q^{\prime } \bar{Q}^{\prime }\)  interactions,
since vector-like quarks interact with \(Z\)  and photon that should be taken into account to check
consistency of the scenario.
Note also that we could not explain muon \(g-2\)  in this scenario since \(Z^{\prime }\)  from \(U(1)_{\mu - \tau }\)  should be heavier than \(\mathcal {O}(10)\)  GeV. Also in Ref.  [1]} we introduced
only vector-like quarks and not vector-like leptons, and the model looks non symmetric.
Thus it is interesting to add vector-like leptons in addition to vector-like quarks in the previous
scenario to make the model look more symmetrical, to explain muon \(g-2\)  and consider loop diagrams associated with \(Z\)  and photon interactions to check consistency for \(b\rightarrow s \mu ^+ \mu ^-\) 
anomalies. We will also introduce two inert complex scalars \(\chi _q\)  (leptophobic)
and \(\chi _l\)  (leptophilic) that are charged under \(U(1)_{\mu - \tau }\)  in such a way that Yukawa
couplings among the vector-like quarks (leptons), SM quarks (leptons) and the inert scalar \(\chi _q\) 
(\(\chi _l\) ) are allowed by gauge symmetries.
